Answer :

Given the radius of a sphere is measured as 9 cm with an error of 0.03 m = 3 cm.


Let x be the radius of the sphere and Δx be the error in measuring the value of x.


Hence, we have x = 9 and Δx = 3


The surface area of a sphere of radius x is given by


S = 4πx2


On differentiating S with respect to x, we get




We know




When x = 9, we have.



Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as



Here, and Δx = 3


ΔS = (72π)(3)


ΔS = 216π


Thus, the approximate error in calculating the surface area of the sphere is 216π cm2.


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